But in a cruel twist for a franchise in the midst of an overhaul, it appears the Mystics could miss out on one of the deepest classes in recent years.

Washington will have the No. 4 pick in next April’s draft, their fate decided by a collection of 14 ping-pong balls in Bristol, Conn. It was the lowest possible selection the Mystics could have received.

Phoenix, which had a 27.6 percent chance to earn the top choice, won the lottery and will select first. Washington had a 44.2 percent chance to get the No. 1 pick.

Washington is looking for its 13th coach, and seventh GM, in 15 years. The Mystics have qualified for the WNBA playoffs, which begin Thursday, six times.

But if they are to return to the postseason, they’ll have to do it without one of the three elite prospects at the top of the 2013 draft board.

Baylor star Brittney Griner, the national player of the year, guided the Bears to an undefeated (40-0) national championship season and is considered the likely No. 1 pick. Delaware forward Elena Delle Donne, the nation’s leading scorer last year, and Notre Dame guard Skylar Diggins are also highly regarded.

Washington finished with a 5-29 record this past season, including a 13-game losing streak to close the year. The Mystics previously selected No. 1 in the 1999 draft, when they selected Chamique Holdsclaw.